For the five centers, the \(z\) -axis of \({\mathbb {E}}^3\)  in the Gibbons-Hawking space consists of the six intervals,
\(I_-=\lbrace (x,y,z)|x=y=0, z<z_1\rbrace \) , \(I_i=\lbrace (x,y,z)|x=y=0,z_i<z<z_{i+1}\rbrace \ (i=1,...,4)\)  and \(I_+=\lbrace (x,y,z)|x=y=0,z>z_5\rbrace \) .
As was previously discussed in [1]}, only particles with the angular momentum of \(l_{\phi _2}=0\)  can move on \(I_1\) , \(I_3\)  , \(I_+\)  but cannot move on \(I_-\) , \(I_2\)  and \(I_4\) .
Similarly, only particles with the angular momenta of \(l_{\phi _1}=0\)  are allowed to move on \(I_-\) , \(I_2\)  and \(I_4\)  but cannot move on \(I_1\) , \(I_3\)  and \(I_+\) . Here, as typical examples, we study two cases of \(j^2\simeq 0.919\)  and \(j^2\simeq 14.8\)  for particles with \(l_{\phi _2}=0\) .
